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3 years ago

What are the values of the three trigonometric ratios for angle L, in simplest form?

Mathematics

2 answers:

Oxana [17]3 years ago

7 0

The correct answer's are:

sin(L) = 4/5

cos(L) = 3/5

tan(L) = 4/3

viva [34]3 years ago

6 0

Answer:

4/5, 3/5, 4/3

Step-by-step explanation:

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A service station will be built in the highway, and a road will connect it with cray. How long will the new road be?

abruzzese [7]

Answer: 24 mi

Step-by-step explanation:

Let the points A, B, C and S represent Alba, Blare, Cray and Service station respectively,

Then According to the question,

We have to find out the line segment CS = x = ?

Now, In the triangles ACB and CSB,

$\angle ACB\cong \angle CSB$ ( Right angles )

$\angle ABC\cong \angle CBS$ ( Reflexive angles )

Thus, by AA similarity postulate,

$\triangle ACB\sim\triangle CSB$

By the property of similar triangles,

$\frac{AB}{CB}=\frac{AC}{CS}$

$\implies \frac{50}{30}=\frac{40}{x}$

$\implies 50x=30\times 40$

$\implies 50x = 1200$

$\implies x =24$

Thus, the length of the new road = 24 miles

7 0

3 years ago

Paul is two years younger than Patricia. Daniel is 25% older than Patricia. Ten years ago, Daniel was 50% older than Patricia. H

Sergeeva-Olga [200]

We have 3 people: Paul, Daniel and Patricia. Let each name denote that person’s current age in years. Remember that % is the symbol for 1/100.

PAUL: (#A) Paul = Patricia – 2
DANIEL:
(#B) Daniel = 125% * Patricia = 125 * (1/100) * Patricia = 1.25 * Patricia
(#C) Ten years ago, Daniel’s age at that time would have been Daniel’s current age – 10. IE “Daniel – 10”.
Ten years ago, Patricia’s age at that time would have been Patricia’s current age – 10. IE “Patricia – 10”.
Ten years ago, Daniel’s age at that time (IE Daniel – 10) was 50% greater than Patricia’s age at the time (Patricia – 10).
IE

Daniel – 10 = 150% * (Patricia – 10)
Daniel – 10 = 1.50 * (Patricia – 10)
Daniel – 10 = 1.50 * Patricia – 1.50 * 10
Daniel – 10 = 1.50 * Patricia – 15
Daniel = 1.50 * Patricia – 15 + 10
Daniel = 1.50 * Patricia – 5

So now we have 3 equations in 3 unknowns:
(A) Paul = Patricia – 2
(B) Daniel = 1.25 * Patricia
(C) Daniel = 1.50 * Patricia – 5

Solve equations B & C simultaneously
1.25 * Patricia = 1.50 * Patricia – 5
1.25 * Patricia – 1.50 * Patricia = – 5
– 0.25 * Patricia = – 5
Patricia = (– 5) / (– 0.25)
Patricia = + 20

So now we can write the 3 people’s ages:
(a) Patricia = 20
(b) Paul = Patricia – 2 = 20 – 2 = 18
(c) Daniel = 1.25 * Patricia = 1.25 * 20 = 25

Finally, we check our solution against the original question. 
Paul is two years younger than Patricia. ……… 20 – 2 = 18 ✔
Daniel is 25% older than Patricia. ……… 25 = 125% * 20 ✔
Ten years ago, Daniel was 50% older than Patricia. 25 – 10 = 150% (20– 10) ✔

Hope that helped :)

5 0

3 years ago

If 6^4x = 82, what is the value of x? Round your answer to three places.

neonofarm [45]

Answer:

$x=0.61485921$

Step-by-step explanation:

The given equation is in exponential form:

$6^{4x} =82$

To find $x$ we need to write it in logarithmic form:

$b^{a} =n$ ⇒ $log_{b} n=a$

$6^{4x} =82$ ⇒ $log_{ 6 } 82=4x$

$2.45943684 = 4x$

$\frac{2.45943684}{4} = x$

$0.61485921 =x$

To prove this, we can substitute the value into the given equation

$6^{4x} =82$

$6^{4(0.61485921)} =82$

$82=82$

Therefore, the answer is $x=0.61485921$

6 0

3 years ago

Solve the system of 2x-5y+z=1 3 y+2z=5-24z=48

motikmotik

A) 2x -5y +z = 1
B) 3 y + 2z = 5
C) -24 z = 48
Those 3 equations you typed were somewhat squished together.
Did I retype those correctly?
Let me know and I'll solve it.

8 0

3 years ago

Ellen has a bag with 3 red marbles and 2 blue marbles in it. She is going to randomly draw a marble from the bag 300 times, putt

sweet [91]

Answer:

No. of times Ellen draws a blue marble = 120

Step-by-step explanation:

No. of red marbles = 3

No. of blue marbles = 2

$\text{Probability of drawing a blue marble = }\frac{\text{No. of possible outcomes}}{\text{Total no. of outcomes}}\\\\P(B)=\frac{2}{5}\\\\No. of draws (n) = 300\\\text{So, total probability = }n\times P(B)\\\\=100\times \frac{2}{5}=120.$

So, the required probability is 120.

7 0

3 years ago

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